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Averaging a representation over a subgroup

Author: R. B. Burckel
Journal: Proc. Amer. Math. Soc. 78 (1980), 399-402
MSC: Primary 22D10; Secondary 43A07
MathSciNet review: 553383
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Abstract: The purpose of this note is to extend a well-known technique for getting a representation of a quotient group from one of the original group. This is usually done by ``integrating'' coefficient functions of the representation over the subgroup, i.e., by applying some mean to them. Hence amenability hypotheses are usually made. None are needed here because the relevant coefficient functions belong to the algebra of weakly almost periodic functions (Eberlein [3]), which is always amenable (Ryll-Nardzewski [5]).

References [Enhancements On Off] (What's this?)

  • [1] R. B. Burckel, Weakly almost periodic functions on semigroups, Gordon and Breach, New York, 1970. MR 0263963 (41:8562)
  • [2] C. Chou, Uniform closures of Fourier-Stieltjes algebras, Proc. Amer. Math. Soc. 77 (1979), 99-102. MR 539638 (80i:43007)
  • [3] W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217-240. MR 0036455 (12:112a)
  • [4] P. Eymard, L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181-236. MR 0228628 (37:4208)
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Keywords: Unitary representation, weakly almost periodic function, mean value for WAP functions, Fourier-Stieltjes algebra (nonabelian)
Article copyright: © Copyright 1980 American Mathematical Society

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